Councillor Brookfield, who was the Leader of the City of Wolverhampton Council, passed away on Sunday 2 July after a brave battle with cancer. He was 57.
People are invited to leave messages in the physical books of condolence available at the Civic Centre and Low Hill Community Hub during normal opening hours, or in the online book of condolence available at Book of Condolences for Cllr Ian Brookfield.
The messages will be presented to Councillor Brookfield's family in due course.
Acting Leader of the Council, Councillor Stephen Simkins, said: "We have received many, many messages of support, love, gratitude and appreciation from across the city and across the country, with friends, colleagues and residents all paying tribute to Ian, and I would like to thank everyone who has shared their feelings in this way.
"If you wish to leave your own personal message, you are invited to do so by signing the books of condolence at the Civic Centre or Low Hill Community Hub, or online, before the end of this week.
“We will be presenting the books of condolence to Ian's family when the time is right and we hope that they will provide some sort of comfort for them at this terribly difficult time."
The council plans to hold a civic event in the autumn to celebrate the life and political career of Councillor Brookfield, and details will be announced in due course.